A numerical solution of the Burgers' equation using septic B-splines

In this paper, numerical solutions of the nonlinear Burgers' equation are obtained by a method based on collocation of septic B-splines over finite elements. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. Numerical solutions of the modified Burgers' equation are also obtained by making a simple change of the suggested numerical scheme for the Burgers' equation. The accuracy of the presented method is demonstrated by two test problems. The numerical results are found to be in good agreement with the exact solutions.